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summary of this topic

Properties of Complex Number Arithmetic

Properties of Complex Number Arithmetic

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 »  Modulus of product is product of modulus.

    →  `|z_1 xx z_2| = |z_1| xx |z_2|`

Modulus in multiplication

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Modulus of product is product of modulus.

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trek

simple steps to build the foundation

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Modulus of product is product of modulus.


Keep tapping on the content to continue learning.
Starting on learning "Modulus in Multiplication". ;; In this page you will learn that modulus of product is the product of modulus.

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2` what is the modulus of product `|z_1 xx z_2|`?

  • `|z_1| xx |z_2|`
  • `|z_1| + |z_2| `

The answer is '`|z_1| xx |z_2|`'.

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2`, the modulus of product
`|z_1 xx z_2|`
`quad quad = |a_1a_2-b_1b_2 + i(b_1a_2+a_1b_2)|`
`quad quad = sqrt(a_1^2+b_1^2)sqrt(a_2^2+b_2^2)`
`quad quad = |z_1| xx |z_2|`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Modulus of Product: For complex numbers `z_1, z_2 in CC`

`|z_1 xx z_2| = |z_1| xx |z_2|`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given `z_1 = a_1+ib_1` and `z_2 = a_2+ib_2` what is the modulus of quotient `|z_1 -: z_2|`?

  • `|z_1| -: |z_2|`
  • `|z_1| - |z_2| `

The answer is '`|z_1| -: |z_2|`'.

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Given z1 = a1+i b1 and z2 = a2+i b2, what is the modulus of product mod z1 multiplied z2?
multiplied
mod z1 multiplied mod z2
plus
mod z1 plus mod z2
The answer is 'mod z1 multiplied mod z2'
Given z1 = a1+i b1 and z2 = a2+i b2, the modulus of product ;; mod z1 multiplied z2 ;; equals mod a1 a2 minus b1 b2 + i b1 a2+a1 b2 ;; equals square root a1 squared +b1 squared ;; square root a2 squared + b2 squared ;; equals mod z1 multiplied mod z2
Modulus of product is product of modulus.
Modulus of Product: For complex numbers z1, z2 in complex numbers, mod z1 multiplied z2 equals mod z1 multiplied mod z2
Given z1 = a1+i b1 and z2 = a2+i b2 what is the modulus of quatient mod z1 divided by z2?
divided
mod z1 divided by mod z2
minus
mod z1 minus mod z2
The answer is 'mod z1 divided by mod z2'

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